Convergence of the variational iteration method for solving multi-order fractional differential equations

Yang, Shiliang; Xiao, Aiguo; Su, Han

doi:10.1016/j.camwa.2010.09.044

Cited by 85 publications

(35 citation statements)

References 32 publications

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“…Most fractional differential equations do not have exact analytic solutions, so approximation and numerical techniques must be used. For example Adomian decomposition method, the homotopyperturbation method, the variational iteration method and the homotopy analysis method [13][14][15][16][17][18][19]. In this paper we use the collocation method for solving fractional Pantograph differential equation …”

Section: Nowadays Notable Contributions Have Been Made Theory and Appmentioning

confidence: 99%

Numerical Approach for Solving Fractional Pantograph Equation

Anapali¹,

Öztürk²,

Gülsu³

2015

IJCA

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In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of linear algebraic equation using Maple 14 and we obtain the coefficients of Taylor expansion. In addition illustrative example is presented to demonstrate the effectiveness of the proposed method.

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Section: Nowadays Notable Contributions Have Been Made Theory and Appmentioning

confidence: 99%

Numerical Approach for Solving Fractional Pantograph Equation

Anapali¹,

Öztürk²,

Gülsu³

2015

IJCA

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“…[1,10,11,12,14,17,18,21,22,25,26]. The investigation of the analytical properties of such systems is often restricted to the case where the orders of the differential operators are rational [5,6,7,16].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of solutions of linear multi-order fractional differential systems

Diethelm

Siegmund

Tuan

2017

FCAA

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In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.

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“…Therefore this method is becoming a very attractive research area and as such, several methods are established. The Adomian decomposition method [4], variational iteration method [5], homotopy perturbation method [6] and predictor-corrector method [7] are some of the more famous methods. In particular, systems of FDEs are considered in [8] where the Adomian decomposition method was employed for the solutions of system of nonlinear fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

Isah

Phang

2016

Open Physics

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Abstract:In this work, we propose a new operational method based on a Genocchi wavelet-like basis to obtain the numerical solutions of non-linear fractional order differential equations (NFDEs). To the best of our knowledge this is the first time a Genocchi wavelet-like basis is presented. The Genocchi wavelet-like operational matrix of a fractional derivative is derived through waveletpolynomial transformation. These operational matrices are used together with the collocation method to turn the NFDEs into a system of non-linear algebraic equations. Error estimates are shown and some illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed technique.

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Convergence of the variational iteration method for solving multi-order fractional differential equations

Cited by 85 publications

References 32 publications

Numerical Approach for Solving Fractional Pantograph Equation

Numerical Approach for Solving Fractional Pantograph Equation

Asymptotic behavior of solutions of linear multi-order fractional differential systems

Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

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